BX from Synchronous Grammars

1. BX from Synchronous Grammars Yingfei Xiong, 2013 In cooperation with Yangyi Wu, Yiming Wu

2. Synchronous Grammar • Invented by the natural language processing community at 60s • Initially for language translation • Normal Grammar (postfix expressions) • N -> N N ‘*’ | N N ‘+’’ | int • Synchronous Grammar (prefix  postfix) • ‘*’ N N <- N -> N N ‘*’ • ‘+’ N N <- N -> N N ‘+’ • int <- N -> int

3. Translation with Synchronous Grammar • Syntax-directed translation • Rules on one side => actions on the other side • N -> N N‘*’ { print(‘*’ N N); } • N -> N N‘+’ { print(‘+’ N N); } • N -> int {print(int);}

4. BX with Synchronous Grammar • Composer Composers <- Compsers -> Composer Composers • Composer <- Composers -> Composer • Name ‘,’ Years ‘,’ Country <- Composer -> Name ‘,’ Country • alpha alpha <- Name -> alpha alpha • year ‘-’ year <- Years -> year ‘-’ year • alpha <- Country -> alpha

5. BX with Synchronous Grammar • Perdita Steven’s framwork • R: source and target can be produced by the grammar

6. A backward transformation m N’ parse parse AST_m AST_n’ Backward merge AST’ print m’

7. BX properties • Hippocraticness • Holds when the grammar is unambiguous • Correctness • Holds since the syntax-directed translation is just the inverse of parsing on the same side • Undoability • Not hold as usual, since there might be information loss during changes

8. Symmetric Lenses • We can construct a symmetric lenses by letting C be the merged AST

9. Extension: dictionary lenses • Composer* <- Composers -> Composer* • key Name ‘,’ Years ‘,’ Country <- Composer -> Name ‘,’ Country • alpha alpha <- Name -> alpha alpha • year ‘-’ year <- Years -> year ‘-’ year • alpha <- Country -> alpha

10. Expressiveness • Comparing with Boomerang • Boomerang is a regular language, unable to handle cases such as “matching the parentheses” • Conjecture: Any lenses expressible by Boomerang is expressible in this approach • Work-in-progress • Several basic lens combinators have been translated into combinators on grammars • Working on dictionary lenses

11. Conclusion • A novel way of constructing BX • Less learning effort • Reuse existing asserts: theories, algorithms and grammars • Potentially more expressive than Boomerang